In this paper we analyze flexible inflation targeting and nominal income targeting as two different monetary strategies in a simple dynamic macromodel. Furthermore we analyze inflation targeting in a two-period time-lag version of the model. The key results of our paper are: First, for both targeting regimes optimal monetary policy response leads to a shock-dependent feedback rule. Second, a demand shock is completely offset by both monetary strategies. Third, in case of a supply shock there is a significant difference between the two different targeting regimes. Under inflation targeting the policy makers face a trade-off between inflation and output stabilization. This trade-off depends on the weight F the policy makers attached to output stabilization relative to inflation stabilization in the loss function. In contrast, under nominal income targeting policy makers face a constant trade-off between inflation and real output growth: An increase in inflation leads to a fall in real output growth by an equal amount. Finally we analyze inflation targeting in a two-period time-lag version of the model. The qualitative results about the trade-off between inflation and output growth remain the same as in the basic model without time lag.